Over the past several years, there has been considerable interest in using optical scatterometry (i.e., optical diffraction) to perform critical dimension (CD) measurements of the lines and structures included in integrated circuits. Optical scatterometry has been used to analyze periodic two-dimensional structures (e.g., line gratings) as well as three-dimensional structures (e.g., patterns of vias or mesas). Scatterometry is also used to perform overlay registration measurements. Overlay measurements attempt to measure the degree of alignment between successive lithographic mask layers.
Various optical techniques have been used to perform optical scatterometry. These techniques include broadband scatterometry (U.S. Pat. Nos. 5,607,800; 5,867,276 and 5,963,329), spectral ellipsometry (U.S. Pat. No. 5,739,909) as well as spectral and single-wavelength beam profile reflectance and beam profile ellipsometry (co-pending application Ser. No. 09/818,703 filed Mar. 27, 2001). In addition it may be possible to employ single-wavelength laser BPR or BPE to obtain CD measurements on isolated lines or isolated vias and mesas.
Most scatterometry systems use a modeling approach to transform scatterometry signals into critical dimension measurements. For this type of approach, a theoretical model is defined for each physical structure that will be analyzed. The theoretical model predicts the empirical measurements (scatterometry signals) that scatterometry systems would record for the structure. A rigorous coupled wave theory can be used for this calculation. The theoretical results of this calculation are then compared to the measured data (actually, the normalized data). To the extent the results do not match, the theoretical model is modified and the theoretical data is calculated once again and compared to the empirical measurements. This process is repeated iteratively until the correspondence between the calculated theoretical data and the empirical measurements reaches an acceptable level of fitness. At this point, the characteristics of the theoretical model and the physical structure should be very similar.
The calculations discussed above are relatively complex even for simple models. As the models become more complex (particularly as the profiles of the walls of the features become more complex) the calculations become exceedingly long and complex. Even with high-speed processors, the art has not developed a suitable approach for analyzing more complex structures to a highly detailed level on a real time basis. Analysis on a real time basis is very desirable so that manufacturers can immediately determine when a process is not operating correctly. The need is becoming more acute as the industry moves towards integrated metrology solutions wherein the metrology hardware is integrated directly with the process hardware.
One approach that allows a manufacturer to characterize features in real time is to create “libraries” of predicted measurements. This type of approach is discussed in PCT application WO 99/45340, published Sep. 10, 1999 as well as the references cited therein. In this approach, the theoretical model is parameterized to allow the characteristics of the physical structure to be varied. The parameters are varied over a predetermined range and the theoretical result for each variation to the physical structure is calculated to define a library of solutions. When the empirical measurements are obtained, the library is searched to find the best fit.
In general, libraries have proven to be an effective method for quickly analyzing samples. Unfortunately, libraries have also proven to have their own disadvantages. One disadvantage results from the fact that libraries must be generated in a reasonable amount of time and must occupy a reasonable amount of space. This means that libraries must have limited range (i.e., the library is limited to a portion of the total solution space). Libraries must also have limited resolution (i.e., there must be some granularity between solutions). These limitations become problematic when test data doesn't closely match the range and resolution of the library being used. If a library has inadequate range, for example, test data may not match any of the library's stored solutions. This same result can occur when a library has adequate range, but the range is incorrectly centered in the spectrum of solutions. Libraries may also have inadequate resolution causing test data to fall between stored solutions. In other cases, libraries may have excessive range or resolution wasting both time and space.
One approach for dealing with this problem is to use the library values as a starting point for the solution and then determine parameters using interpolation or estimation procedures. U.S. Pat. No. 5,867,276 describes a system of training a library to permit linear estimations of solutions. Another form of interpolation can be found in U.S. Patent Application 2002/0038196, published Mar. 28, 2002. PCT WO 02/27288, published Apr. 4, 2002 suggests using a coarse library and a real time regression approach to improve results. The latter documents are incorporated by reference.
Even using the above approaches, the initial libraries in working optical metrology systems are seldom optimal for either range or resolution. This follows because optimal values for range and resolution are difficult to predict as libraries are being built. Inevitable errors in these predictions mean that libraries are never entirely efficient at analyzing test results. Errors of this type often compound, as libraries are used and operational parameters change or drift. In these cases, libraries become increasingly out of sync with their optical metrology systems and increasingly inefficient at analyzing test results. A more ideal solution would be to develop a system that adapted libraries to the actual test results generated by optical metrology systems.